These are approximate equations for deducing the complex dielctric constant values of mixtures, assuming the theoretical full-density material dielectric values are known. Used in reverse, one can extract full density values from measurements on two-component mixtures, the most common of which is air-solid mixtures .

Note: This must be used in a full "complex math" form - ie., using j as SQRT(-1)

Reference:

• (1) Looyenga, H. 1965 Physica 31 , pg 401-406
• (2) Landau L D and Lifshitz E M 1960, Electrodynamics of Continuous Media. Vol. 8, Course of Theoretical Physics (Oxford: Pergamon)

Special Case of Air ( or a Gas) Being One of the Two Components :

If material #2 is air, then ε₂ is unity, and the mass of material #2 is ~ zero . In this case, the density of the mixture is that of material #1 (theoretical density) multiplied by the volume fraction of material #1.

Outline of Preferred Laibinis Mixing Equations for Liquids

Equations Recommended by Laibinis for Determining the Debye Parameters for a Mixture Of Two Liquids

Reference:

• “Mixing Rules for the Dielectric Properties of Solvent Mixtures at Microwave Frequencies”, J. Lou, T.A. Hatton, and P. E. Laibinis , Microwave: Theory and Applications in Materials processing IV, Ceramic Transactions, Vol. 80, Pg 115, Edited by D. Clark, W. Sutton, D. Lewis

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